Question

Vessel A contains CO(g) at 0°C and 1 atm. Vessel B contains SO2(g) at 20°C and 0.5 atm. The two vessels have the same volume. a) Which contains more molecules? b) Which contains more mass? c) In which vessel is the average kinetic energy of molecules higher?

Answer 1

A. There are 1.86 times more moles of gas A (CO) than gas B (SO2).

There are more molecules of CO than SO2

B. Container B (SO2) contains more mass.

C. Vessel B has the highest average kinetic energy of the molecules

Step-by-step explanation:

The Ideal Gas Law says:

PV = nRT, where P, V, and T are pressure, volume, and temperature (in Kelv1n). R is the gas constant and n is the moles of gas.

The volumes are the same, so lets choose 1 L as a starting point.

`n_(a)` is the moles of gas in container A

`b_(b)` is the moles of gas in container B

Vessel A:

PV = nRT

(1 atm)*(1 L) =
`n_(a)`*(R)*(273K)

Vessel B:

PV = nRT

(0.5 atm)*(1 L) =
`n_(b)`*(R)*(293K)

Lets rearrange both equations to isolate the moles, n, of each gas.

Vessel A:

(1 atm)*(1 L) =
`n_(a)`*(R)*(273K)

`n_(a)` = ((1 atm)*(1 L) =)/((R)*(273K))

Vessel B:

(0.5 atm)*(1 L) =
`n_(b)`*(R)*(293K)

`n_(b)` = ((0.5 atm)*(1 L))/((R)*(293K))

Now lets find the ratio of
`n_(a)` /
`n_(b)`

`n_(a)` /
`n_(b)` =[((1 atm)*(1 L) =)/((R)*(273K))]/[((0.5 atm)*(1 L))/((R)*(293K))])

Rearrange and solve:

`n_(a)` /
`n_(b)` =[((1 atm)*(1 L) =)/((R)*(273K))]/[((0.5 atm)*(1 L))/((R)*(293K))])

`n_(a)` /
`n_(b)` =[((1 atm)*(1 L) )/((R)*(273K))] * [((R)*(293K))/((0.5 atm)*(1 L))])

`n_(a)` /
`n_(b)` =[((1 )*(1 ) )/((273))] * [((293))/((0.5)*(1 ))])

`n_(a)` /
`n_(b)` =[(1 )] * ((293/273))/((0.5)*(1 ))])

`n_(a)` /
`n_(b)` =(1)*(0.932)/(0.5)

`n_(a)` /
`n_(b)` = 1.86

A. There are 1.86 times more moles of gas A (CO) than gas B (SO2).

There are more molecules of CO than SO2

B. Molar masses:

CO = 28 g/mole

SO2 = 64 g/mole

The ratio of molar masses, SO2/CO is (64/28) or 2.28

[1.86x moles CO)/(1x moles SO2) * (28/64) = 0.81

Container B (SO2) contains more mass.

C. Vessel B has the highest average kinetic energy of the molecules since it is at the higher temperature. (20 C vs, 0 C).